Profit & Loss – Advanced Study Notes (MIT‑Level)
Target Audience: UPSC EPFO aspirants
Level: Advanced (University‑level)
Format: Markdown, self‑contained, rigorous, with edge cases & a challenging problem.
1. Foundations
| Symbol | Meaning | Units |
|---|---|---|
| (C) | Cost price of one unit | ₹/unit |
| (S) | Selling price of one unit | ₹/unit |
| (Q) | Quantity sold | units |
| (P) | Profit / Loss on one unit | ₹/unit |
| (\pi) | Profit / Loss on the whole transaction | ₹ |
| (p %) | Profit % or Loss % | percent |
Profit / Loss (per unit)
[
P = S - C
]
If (P > 0) → profit, (P < 0) → loss.
Total Profit / Loss
[
\pi = (S - C) \cdot Q
]
Profit %
[
p% = \frac{S - C}{C} \times 100
]
Alternate definition (margin)
[
\text{Margin}\